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Wednesday, 16 October 2013

Understanding Part 1: Pictures §138-142

As
I discussed in my previous post, a rapid series of modulations brings
us to the topic of understanding when, at the end of §138,
the interlocutor says:

But we understand the meaning
of a word when we hear or say it; we grasp the meaning at a stroke,
and what we grasp in this way is surely something different from the
'use' which is extended in time!

This
is probably the strongest objection so far to Wittgenstein's account
of meaning. Its power stems from the way it ties into various
extremely tempting ideas about the process of communication. Above
all, it suggests that understanding is some kind of thing that
we acquire when we learn the meaning of a word, and which is
subsequently represented to us whenever we hear that word.

The
appeal of this idea is bolstered by various simple reflections. When
we come to know the meaning of a word we gain understanding –
so we must've gained something! Likewise, if we don't know the
meaning of a word then we lack understanding – so
“understanding” must be whatever it is we lack. And although we
might exhibit understanding in performance (eg, by using a word
correctly), that is not understanding itself; it is merely
evidence from which others can infer that we do indeed possess
understanding.

Moreover,
when we hear words we are immediately aware of our understanding. The
words strike us in a quite vivid and particular way. We don't simply
hear sounds or see ink-marks on a page (or shapes on a computer
screen) – we hear (or read) language. We experience
the meanings that it conveys. To see that this is so, just compare
the case of reciting a passage we don't understand (having learnt it
parrot-fashion, perhaps) with that of reciting one whose words are
familiar to us. Surely it is undeniable that what happens inside us
in the two cases is completely different?

Such
considerations present a challenge for Wittgenstein. When we
understand a word we understand its meaning. But what we grasp in the
instant of understanding doesn't seem to be anything like a use.
(And, in any case, is use something that could
be grasped in an instant?) But if what we grasp isn't use then
meaning can't be use.

2.
Pictures and their application

Wittgenstein
begins his assault on this appealing conception by considering the
notion that understanding is a picture
that comes before our mind when we hear a word (§139).
It's a natural enough place to start given that his early philosophy
propounded what's called “the picture theory of language”.
Moreover, that theory was itself a refinement of a venerable
philosophical position dating back at least as far as Locke's Essay
Concerning Human Understanding.
In my last
post I gave a rough sketch of the account of communication that
the picture theory tends to suggest. It might be helpful to repeat
that here:

Person
A has the thought, in the form of a picture, that things are
thus-and-so. She wants to communicate her thought to B so she
“converts” it into a proposition: she speaks, writes, uses
sign-language or Morse code, etc. The words she uses relate to the
elements of her picture and are arranged in a similar fashion. Next,
B perceives A's proposition and he re-converts it into a thought.
That is to say, the words he hears (reads, etc) produce a picture in
his mind. That picture is his understanding of what A said. If he has
the same picture he has understood correctly; if he has a different
picture then he has misunderstood (and if he has no picture at all
then he has not understood at all). The correctness of his picture
can be inferred from his behaviour. Of course, we can't be sure
B's picture matches A's but so long as he fetches the right object
(etc) then it is reasonable to assume that it does.

In
attacking the idea of understanding as a picture, it is this last
part of the account that Wittgenstein focuses upon: the link between
the picture and subsequent behaviour. He points out (§139)
that, whatever might happen in our minds, our behaviour is still a
criterion for understanding. If someone consistently uses
a word incorrectly then we say that he or she doesn't understand its
meaning. So understanding is clearly bound up with use in some sense.
But if understanding is a mental picture then what is the link
between that picture and use? “Can what we grasp at a
stroke agree with a use, fit or
fail to fit it?” (§139.)
Wittgenstein suggests an answer to his own question: let's assume
that when I hear the word “cube” I get a picture of a cube in my
mind. If I point to a cube my use fits the picture, but if I point to a
triangular prism instead then my use has failed to fit the picture.

At
first blush this seems straightforward, but Wittgenstein argues that
it will not do. The problem is: who is to say that pointing to the
triangular prism actually is
an incorrect use of the picture?

His objection is couched in terms of the picture's “method of projection”.
I assume that's a glance back to Wittgenstein's time as an
engineering student and refers to techniques used in technical
drawing. I'm afraid I have roughly zero understanding of such things
(I looked up geometric projection on Wikipedia and it didn't help)
but there are other ways of making the same point. Basically it comes
to this: a picture by itself stands in need of a method of
application. If no method is
stipulated then it's impossible to say whether a picture has been
used rightly or wrongly.

So,
returning to the example of “cube”, the word presents me with a
picture:

I
then look about me and spot a triangular prism. I realise that in
both cases they have equal ends and parallel rectilinear figures and
that their sides are parallelograms. I therefore point to the
triangular prism because, in that sense,
it is the same as my picture. In other words, I have used my picture
as an example of a prism (for a cube is a prism too). That might seem
an unusual way of
applying the picture, but who is to say that it's wrong?

To
see how far use can deviate from expectation, consider the following
example: I present someone with a dog and an iPhone. I then give him
a photo of the dog and ask him to choose which of the two items it
most resembles. He chooses the iPhone because, like the photo, you
can hold it in your hand, put it in your pocket, etc. Of course most
of us would automatically choose the dog, but that is only because we
are already familiar with the activity of picking things out from
photos. It is something we’ve done countless times and so it
probably wouldn’t even occur to us to use the photo in a different
way. But there is nothing that says choosing the dog must
be the correct response in all circumstances. Indeed to someone with
a different upbringing from ours the dog might seem an absurd
choice.

The
picture, don't forget, is not being cast as an aid
to understanding; it is supposed to be the thing itself.
But it's hard to see how it can play that role when it provides no
standard of correctness. If this observation seems familiar, that's
because it is closely analogous to the point made about ostensive
definition in relation to meaning. There, it was supposed that
the sample by itself
could establish a link between word and object, that it was
completely unambiguous and therefore unmistakable. But it turned out that it
only functioned as part of an established practice of describing the
rule for the use of a
word. And it's a very similar story in the case of the picture (which
is, after all, a kind of mental
sample). We have the sample, but what we lack is the application. (I
should also mention that as well as looking back to ostensive
definition this point also anticipates aspects of the discussion of
rule-following. See, for example, §201:
“if every course of action can be brought into accord with the
rule, then it can also be brought into conflict with it. And so there
would be neither accord nor conflict here”. This overlap should not
be surprising; the concept of understanding is internally connected
to the concept of meaning. Each helps define the other. And they are
both closely bound up with the concept of rule-following.)

3. Compulsion

The
reminder that a picture can be used in various different ways also
serves to highlight (and undermine) another temptation regarding
understanding as an “inner” phenomenon: the assumption that the
relation between representation and what is represented somehow takes
care of itself. We don't need to stipulate a method of application
because the picture does it for us. It's especially easy to think
like this when we focus on the immediacy and fluency with which we
usually understand language. We don't have to struggle to grasp the
meaning – in fact, it's impossible for us not
to understand. It's as if the picture somehow carries its meaning
within it, like a kind of spirit, and exposure to the picture
transfers this spirit to us, so that we cannot help but see the
picture as an image of this
object. The words (or rather the images they produce) force
an application on us (§140).

In
the Tractatus this
seems to be regarded as a kind of logical
compulsion. So long as picture and fact share the same logical
structure there cannot
be doubt about what's represented. Of course, this idea is exploded
by the simple observations in §139
(it is, in fact, another example of a rule
misrepresented as a necessary feature of the world). But there
are other ways of presenting the idea of compulsion. As Wittgenstein
says in §140,
“we might also be inclined to express ourselves like this: we're at
most under a psychological, not a logical, compulsion”. He then
adds a typically cryptic coda: “And now, indeed, it looks as if we
knew of two kinds of case.” What's he getting at here?

I
think this is a warning against defending a preconception by taking
refuge in theoretical explanations. We assumed we were under
compulsion; the idea that it was a logical one has proved empty, so
now we say it must be “some other kind”. And, happily, we hit
upon the notion of “psychological compulsion” as a
plausible-sounding alternative. (Already we can see the bewitching
idea of a mental mechanism
looming on the horizon.) But notice how vague all this is! How much
do we actually know about psychological compulsion? Is it clear
that this is an example of it? And how do we propose to find out?
Will we be conducting field experiments or can we decide things from
our armchairs? Isn't the idea of psychological compulsion just a
guess – and a guess
that invokes a mysterious realm of mental structures, subconscious
computation, and so forth?

There's
a second, perhaps more fundamental, issue. We've been attempting to
clarify the concept of understanding, but now it looks as if we're
sliding into a quasi-causal explanation. But that's like trying to
find out what a watch is
by examining the structure of its cogs and springs. Such an
investigation may be useful in various ways, but it won't tell you
anything about the role watches play in people's lives. For that you
need to describe their use,
not their internal mechanisms. The notion of compulsion tempts us
away from a conceptual investigation towards an ersatz scientific one
which is doomed to failure from the outset.

Well,
Wittgenstein may be alluding
to such thoughts in §140,
but he doesn't elaborate on them at this point. Instead, he sidesteps
the quagmire of compulsion and brings things down to earth: “our
'belief that the picture forced a particular application upon us'
consisted in the fact that only the one case and no other occurred to
us.” This, of course, is a move from the theoretical back to the
descriptive. Why no
other case occurred to us is not Wittgenstein's concern. But the fact
that they didn't made it seem like the picture could only be applied
in one way even though (as we now see) that's not true at all.

It
is this observation that subsequently allows him to answer the
question in §139:
how can what's grasped in an instant fit or fail to fit a use?
“[T]hey can clash in so far as the picture makes us expect a
different use; because people in general apply this
picture like this”
(§141).
What seemed to be a mysterious (perhaps impossible) relation between
two entirely different phenomena turns out to be remarkably simple
and ordinary.

4. Building in the
application

Maybe,
however, compulsion isn't the only answer. Perhaps we could build the
application into the picture itself, thereby allowing it to perform
its allotted function. Wittgenstein considers this in §141.
“How,” he asks, “am I to imagine this?” The answer he
suggests is a picture of two cubes with lines of projection between
them. Something a bit like this perhaps:

Actually,
I don't think that quite works. The cube on the left presumably
represents the mental image and the one on the right represents
actual cubes in the world (and the lines attempt to show the relation
between the two). But we no longer have the mental image that the
left-cube pictures! So we're going to need two separate images:
first, the picture of the cube by itself and, second, the picture of
the two cubes showing how the cube in the first picture is to be
applied. But this raises a further problem: how do we know the
relationship between these two images? How do we know that the
left-cube in the second image represents the cube in the first image?
Aren't we going to need a third
image depicting the relation between the two we already have? And
won't that in turn require a fourth and fifth image linking the third
image to the first and second ones? And so on.

In
a roundabout way this comes to the same objection that Wittgenstein
makes about his own proposed image: whatever its content it will
still just be another picture, and will therefore stand in need of an
application. It's not simply that the initial picture didnot provide its
application (as if that were a kind of oversight); it could
not do so. Application cannot be
provided in that way.

Is
Wittgenstein claiming, then, that there's no such thing as an
application coming before one's mind? Of course not, but (he reminds
us in §141)
understanding what that
amounts to involves looking at the use of the phrase “the
application came before his mind”. It does not
involve a doomed attempt to posit a hypothetical picture with
miraculous powers. Instead of analysing the phrase himself, however, Wittgenstein leaves it up to us investigate. I think it's worth
having a go because the conclusions it suggests (to me, at any rate)
tie in with many of the points he will shortly be making about other
accounts of understanding. Here's what I came up with:

a. Suppose I've been
teaching someone to use mathematical formulae. Now I show her the
series 0, 1, 1, 2, 3, 5, 8 and ask her to continue it. She ponders
for a while and then cries “I've got it!” I ask her what's
occurred to her and she writes down the formula “Fn = Fn-1 + Fn-2”.
Then she correctly continues the series. That would count, I think,
as an example of the application coming before her mind. Something
occurred to her and it helped her continue the series.

b. However, it would also
count if, instead of the formula, she writes down “Each new number
is the sum of the previous two”. So what comes before her mind
needn't be one specific thing.

c.
But suppose instead when I show her the series she simply says “Oh,
that's easy!” and correctly continues it: “...13, 21, 34, 55...”.
And when I ask what occurred to her she says “Nothing – it was
obvious.” (Perhaps she's worked through the series numerous times
before.) Here no
application came before her mind; she just knew what to do. In other
words, correct performance by itself is not a sufficient criterion.
Did she understand my
order to continue the series? Yes, but that shows you can understand
something without an
application coming before your mind.

d.
Finally, suppose that she writes down the formula as in the first
example, but then has no idea how to continue the series. It later
transpires that she'd previously seen the formula written below the
series and that's why it occurred to her. Here again the application
has not come before her mind even though what occurs to her – the
formula – is exactly the same as in the first example. So correct
performance might not be sufficient, but it's clearly important.

But
what, then, is the difference between (a) and (d)? From the point of
view of the criteria for the phrase “the application came before
her mind”, the difference is not what's in her mind but her past
experiences: her education, training and so on. The formula only
counts as the application in the right circumstances.
We might sum up all these reflections in the following way: however
you slice it, understanding involves more (and sometimes less) than
an application coming before one's mind.

5. Conclusion

A picture cannot fulfil
the role of understanding by itself. This is not to deny that at
least sometimes a word can bring an image before our minds, nor that
the image might help us to use the word correctly. But it cannot
show that we have used the word correctly; it supplies no
method of application and hence no standard of correctness – and
the criteria for applying the term “understanding” are closely
bound up with correct usage.

However, the appeal of
supposing understanding to be an inner “Something” is not so
easily dispelled. Thus, for example, we might think that (questions
of application aside) the pictorial account of understanding is
implausible simply because it doesn't seem to match what actually
happens. When we hear someone speak we don't get a torrent of
pictures running through our minds one after the other. Yet instead
of making us abandon the idea, this objection typically leads to
attempts at refining it. We might wonder, for example, if the
pictures are somehow unnoticed. Do they go by too fast? Are they
perhaps unconscious? And need they be conventional images at
all? Mightn't they take a form that we wouldn't easily recognise as
pictures – formulae, for example? Now comes the thought that what
we're really talking about is something that allows us to compute
the correct output for a given input. And if that's the case, then
isn't “understanding” a question of having the right mental
structure – one that facilitates correct responses? And need
this structure actually be mental? Couldn't it be a state of
the brain? And so on.

It is these types of
“refinement” that Wittgenstein considers in the remaining
sections on understanding. They all, I think, flounder on the point
already made: “understanding” is bound up with application, and
correctness of application can only be given by an established
practice. Nevertheless, it is important for Wittgenstein to
deal with these new variations because otherwise the suspicion will
remain that he has been over-hasty. The prejudice in favour of the
inner “Something” is deep-rooted; digging it out requires tracing
it through all its manifestations. So that's the next post.

23 comments:

Caveat: this comment addresses in some detail W's use of the concept of "projection". One not interested in that should move right along - nothing to see here.

Disclaimer: I'm skeptical about "pictures in the mind", what I take to be the same as "mental images". In particular, there are reasons to doubt that they have causal efficacy, in which case they couldn't affect or effect behavior. I'm also skeptical about things being "brought before the mind" since that smacks of the long since discredited Cartesian theater. However, since the game here is PI exegesis rather than brain physiology, I'll play along.

Despite having a fair amount of familiarity with the concept of projections, I found W's references to them confusing. Here's my best guess at what he had in mind in §139. A cube can be considered to be a square prism: square top and bottom with sides that happen also to be squares of the same size. If one assumes monocular viewing of a square prism or of a triangular prism from a point such that the line-of-sight (LOS) bisects a vertical edge and the outline of the prism has lateral symmetry with respect to that edge, then the prism will appear to be a planar figure comprising two parallel horizontal lines the ends and center of which are connected by three perpendicular vertical lines. The standard parallel projection of a prism (or other object) reverses the idea of LOS and involves mapping each visible point on the prism onto a plane that is perpendicular to the LOS by drawing lines that are parallel to the LOS and intersect the plane.

Assuming certain dimensions of the triangular prism relative to those of the square prism (AKA "cube"), the mental images formed by viewing the prisms from the same point on the LOS will be identical. So, the mental image of the cube as if it were seen from that perspective could indeed cause one to point to a triangular prism that actually is seen from that perspective.

But what does that have to do with the scenario as described in §139 in which it is assumed that the heard word brings to mind a mental image of a cube? It's hard to imagine that such an image would be of a cube viewed as described above rather than as depicted in the post. Perhaps someone who has done a lot of drafting might think of a cube in terms of projections, but the one described above almost certainly wouldn't be among them.

And I don't understand the discussion of methods of projection in §141 at all. What is including such a method in "what comes before the mind" even supposed to add? Eg, in the case of the two prisms, knowing the methods of projection whether onto a plane or onto a retina doesn't help at all in distinguishing them.

Thanks for the account of projection. I don't understand a word of it, but it may help others! :)

You might be better off ignoring the issue of projection (like you, I don't think it's very helpful) and concentrate instead on the method of application - ie, how a picture is to be used. That's the real problem Wittgenstein identifies. Moreover, bear in mind that his point is a logical one - it's not concerned with scientific theories of cognition. It's about the criteria for using the word "understand".

As for the Cartesian theatre of the mind, you're right to be sceptical and Wittgenstein's attack has clear implications for Descartes' notion of "mind". (Obviously, there'll be much more along those lines when we get to the private language argument.) If the concept of understanding cannot be divorced from the idea of a rule-governed practice then Descartes is clearly in trouble. But note! Wittgenstein's attack also has clear and negative implications for conceptions of understanding as "dispositions", "states of mind" or, indeed, "brain-states". He's started off attacking the notion of pictures but his real target is the whole idea the understanding is ANY kind of "inner" thing.

I certainly don't mean to badger you, but basic parallel projection isn't at all conceptually difficult. So, I'll persist for one more comment

Orient an opaque cylinder so that it's pointing at a blank wall (ie, its central axis is perpendicular to the wall). Shine a small flashlight directly on the end of the cylinder further away from the wall. The circular shadow that is cast on the wall is essentially the cylinder's projection in the direction of the wall. Do the same with a square oriented so that one side is perpendicular to the wall. The square shadow that is cast on the wall is essentially its projection in the direction of the wall. In essence, the light is extending a cross section of each object to the wall.

Real projection of more complex objects just adds more detail to the projected outline, eg, features of the surface facing the wall such as lines, corners, etc So, if on the side of the square facing the wall there were a small raised triangle, the real projection would include a two dimensional triangle appropriately positioned in the square outline.

That's it. Hope that helps.

Now I'm especially eager to move on to the next sections of PI. Since I think of all so called "mental states" (eg, belief) as interpretable in terms of actions or dispositions to act, which are clearly brain states (specifically, neuronal networks including motor neurons), I have to assume that W has some concept of "understanding" other than mine.

the difference is not what's in her mind but her past experiences: her education, training and so on.

I enthusiastically second this sentiment. I'd argue that the latter is reflected in her brain configuration in the form of a disposition to respond a certain way.

(c) represents one extreme of experience. Either the subject has seen the series a time or two and has essentially photographic memory, or has for some reason had exposure to it sufficient for her to memorize it, AKA, develop a disposition to produce a continuation of a segment of a familiar series.

(a) represents the other extreme - no prior knowledge of the series but a learned disposition to look for rules that reproduce seemingly arbitrary series of numbers.

I represent something of a composite of those. Due to my background, my immediate disposition was to think "that's probably a Fibonacci series" (perhaps prompted partially by the "F" in (a)'s formula) and then to apply the defining formula to confirm or refute that hypothesis.

The common denominator among these from my perspective is that nothing "comes before the mind", but instead different learned behavioral dispositions get triggered by neural activity consequent to visual sensory stimulation due to being shown the series.

Question: which, if any, of the subjects "knows" that the segment is the beginning of the Fibonacci series?

My Sellarsian answer is that only those who can give reasons convincing to a peer group that the series will continue indefinitely in the prescribed way. That seems clearly to eliminate (c) and (d). (a) is less clear - she knows the formula and that it works for the segment shown, but why think the segment if extended would continue appropriately? Since all I added was the name that corresponds to the formula, I'm no better off than (a). So, it appears that no one really "knows" that it's the Fibonacci series. To know that it seems one would need additional information, eg, assurance that the series segment was generated using the Fibonacci formula and would on request be continued as long as necessary using that formula. But are even those reasons sufficient?

Regarding your first point about the disposition, that may or may not be true - it's a conjecture or hypothesis. The important thing, though, is that it's the circumstances which govern the use of the phrase "the application came before her mind". But possession of (or lack of) a particular neural state is not one of the circumstances taken into account.

In which example does she know it's the Fibonacci series? Potentially all of them. But deciding the issue is a matter of clarifying the the criteria for using the phrase "she knows it's the Fibonacci series". Typically, that's a matter of her correctly naming the series - and it's possible that she might be able to that in all four examples.Of course, there are other senses of "knowing it's the Fibonacci series" (eg, ones that would require correct application of the series). Which sense was relevant would depend on why you were asking if she knew - ie, the circumstances in which the question arose.

Regarding the question as to whether anyone really "knows" it's the Fibonacci series, the doubt seems to me to be founded on a sublimated conception of "knowing". It's as if an explanation has to forestall all possible mistakes for all time. But that's not how explanation functions, nor does the ascription of "she knows x" require that. We set up a rule. If things go smooth then nothing else is needed. If things break down we give further explanations and try again. If things keep breaking down no matter what we do then our ability to use the rule has come to an end. But normally this doesn't happen. So the effectiveness of explanation (and the knowledge it brings about) depends on regularity - both in the world and in human reactions.

This is the point of section 42. I didn't cover that section in my post because it glances ahead to the rule-following argument (see especially sections 240-242). But actually Wittgenstein hints at this in the very first section of the book: "Explanations come to an end somewhere".

An interesting discussion! On the difference between a) and d) I was wondering why you focussed so much on the past - I would have thought that what shows that something relevant came before her mind is what she then goes on to do, so what matters is her future action! In fact, when you describe the different cases you do differentiate them on this basis. So we say someone has understood something when they go on to give a correct explanation. When they give a different explanation, we say they have understood wrongly or at least differently; and when they can give no explanation, we would (normally) say that they have not understood. To be slightly controversial, one could argue that the past is irrelevant - it is certainly not what we investigate when we want to find out whether the person truly has understood (or does indeed know how to continue the sequence). If a lion or a monkey showed signs of being able to continue the sequence correctly, proving that they had not got a GCSE in mathematics would not be a decisive way of proving that they were not able to continue the sequence correctly and had not understood it when they stopped hesitating and start to indicate the next items in the series :-)

My reply to Charles probably did emphasise the past too strongly - you're right that what she goes on to do is crucial, but (I think) her past plays a role in how we evaluate what she goes on to do.

So, in (a) it's important that she had received a particular type of training, had used mathematical formulae before, etc - and so citing the formula as the key occurrence makes sense in that context. It's part of what allows us to say "the application came before her mind".

If she'd previously shown the ability to use a formula like "Fn = Fn-1 + Fn-3" and now she says "I've got it!", writes down the formula for the Fibonacci series yet then can't actually continue it we'd think something very strange was going on. It would be an abnormal case and we wouldn't quite know what to make of it. We'd want to investigate further.

But in (d), let's assume she hadn't received the same training or shown the same ability. But we don't know this - we're testing her to see what she can do. She writes down the correct formula and it looks like it's a case like (a). But now she can't continue the series. It turns out the formula occurred to her simply via association (she'd seen it written beneath the series and knew enough to grasp that using the formula was a way to generate the series, but didn't know how to actually use it). This subsequent revelation about her past circumstances helps make sense of her inability to continue the series. Here, I think, what happens before and after her failure kind of go together in helping us decide whether this was an example of the application coming before her mind.

Finally, suppose she was someone who you knew for a fact had never been taught about formulae - she'd never even heard of them. You show her the series, she says "I've got it!", writes down the Fibonacci formula and continues the series correctly. That would be completely bizarre, wouldn't it? I don't think I'd know what to make of such a case at all. Clearly she understands the series, but the role of the formula in helping her continue it is completely opaque to me.

I agree - her giving the formula will convince us that she does indeed know how to go on if she has had some mathematical training and not had a nervous breakdown etc. If we knew she had not had any such training, then we might well not be sure what to make of her citing the formula and want to test a bit more to see if she can indeed continue correctly. If she could, it certainly would be weird, but then mathematical savants are also pretty spooky :-)

Also, I think we should be careful to distinguish between a) "She understands how to continue the series" and b) "She understands how to continue the series because the application came before her mind".

With (a), as you point out, the proof of the pudding is very much in the eating. If she can consistently do it then that's about all you need.

But with (b) I think it's a bit more complicated. You need a bit more scene-setting. And that includes (or can include) her past experiences.

From the post: the difference [between (a) and (d) is their] education, training and so on

to which I added: which are reflected in ... brain configuration in the form of dispositions to respond a certain way.

The response to that was:

that's a conjecture or hypothesis. The important thing ... is ... the circumstances which govern the use of the phrase "the application came before her mind". But possession of (or lack of) a particular neural state is not one of the circumstances taken into account.

As the two cases are described, the "difference" in question is behavioral - applying or not applying the formula. We seem to agree that behavior is influenced by personal history. But how could past history affect current or future behavior other than via "learned" (via brain plasticity) neuronal structures? Admittedly, details about such structures are currently speculative, but that they must exist seems self-evident.

And independent of physiological considerations, since whatever a person is doing or experiencing depends on extant relevant circumstances, among which are the person's physical state, what justifies excluding their neural state?

I sympathize with wanting to avoid unnecessarily getting into the physiological nitty-gritty. But trying to explore the phenomenon of something "coming before the mind" inevitably raises questions like: to what phenomenon does that phrase refer; if such a phenomenon actually does occur; and if so, how and why. Those are scientific questions which invite scientific speculation.

Or perhaps I'm missing the point since "an application coming before the mind" isn't an expression to which I can ascribe any meaning.

I think the nub of the matter here is the difference between an empirical investigation and a conceptual one. For Wittgenstein, what we need to clear up puzzlement over understanding is a clear view of how that word is used - because that is what will show us what we mean by "understanding". When do we say "I understand", "he understands" and so on? What (in other words) are the criteria for the correct application of the term?

Now, it seems clear to me that when I say "He understands" I don't do so because of any knowledge that I have about the workings of his brain, or about the workings of brains in general. I do so on the basis of his performance and the context of his performance. None of that involves an inference about his neurological state.

Of course, it might lead me to wonder about the physical underpinnings of his performance and that might, in turn, lead me to strongly suspect that some kind of neurological happening was involved. But that is an entirely different type of investigation; it doesn't tell us what understanding is. We don't, for example, say "I think he understands, but to be sure I'd have to find out a lot more about his brain". Nor do we say "I think I understand, but I'd have to find out a lot more about my brain to be sure". (Compare that to "I think he's had a stroke".) And nor do we say "I have a theory about what the word 'understanding' means, but I won't know what it really means until neuro-scientists have better explained the workings of the brain."

In certain circumstances it is correct to say "he understands" and it is by describing those circumstances that we get a better grasp of what understanding is - ie, what the word "understanding" means. But those circumstances do not include inferences about neurology or brain-states. After all, young children can use the word "understand" correctly; are they making inferences about their brain-states?

OK, I think I can respond to that comment (ie, I intend to behave as if I "understood" your comment!) I'm all for addressing so called "mental" issues in behavioral terms to the extent possible. In fact, I think of "understanding" a sentence in terms of whether a hearer's responsive behavior is consistent with the behavior the speaker intended to evoke. (Ie, it's up to you to determine whether I really did "understand" your comment.) However, I see a behaviorist approach as no less "empirical" than the brain physiologist's approach. Both involve evidence observed from a third person perspective.

Whatever "coming before the mind" might mean, it's a first person phenomenon that is experienced rather than observed (ie, no Cartesian theater ). First person reports of experienced mental activity even from experts is suspect, and from others is probably worse than useless due partly to common misconceptions about such experiences (in particular, mental imaging). Hence, speculations about what "comes before the mind" of another person seem hopeless.

Relating all this to your test subjects, the observable response common to subjects A and D is producing the defining formula for the Fibonacci series. Using my interpretation of understanding, A "understood" your request as evidenced by her using the formula to provide one possible continuation of the provided fragment as you presumably intended. D didn't as evidenced by her failure to do so. What did or didn't "come before the mind" is unknowable from a third person perspective and in any event seems irrelevant.

Clearly, my interpretation of "understanding" diverges from the common one, which I take to be the successful conveyance of information (syntax) without regard to what is done with the information (semantics). Applying the common interpretation, one could assume that D understood your request but being unable to fulfill it, tried to con you by just providing a formula (from her perspective, a meaningless symbol sequence). But that interpretation disconnects the hearer's understanding from the speaker's intent: she understood you but didn't behave as you intended. Of course, that's a common occurrence, but to ascribe successful understanding to it ignores the role of the purpose of the request. That seems to me inconsistent with "meaning as use". A tool isn't "used" in an abstract sense, it's used to effect a result. The tool is used successfully if the intended result is effected.

Now suppose I say sentence S with the intent that you react in a way different from the way most hearers would. And assume that because of a personal characteristic of yours of which I'm aware, you do react as I intended. Applying the common interpretation of understanding, you didn't understand S notwithstanding that you acted as I intended. But applying my interpretation, you did "understand" S. This seems preferable if one considers effecting an intended result primary, the choice of tool secondary.

Your last two paragraphs essentially give examples of what I suggest avoiding: mixing the psychological and physiological vocabularies carelessly. Of course injecting brain physiology into discussions that are essentially about linguistic practice is inappropriate. But IMO, so is speculating about underlying mental activity.

Just out of curiosity, do you consider "the difference [between (a) and (d) is their] education, training and so on" less hypothetical than "the difference is in their neurological structures"?

As you might've guessed, although Wittgenstein talks about behaviour, he doesn't mean that in a Behaviourist sense. In fact, he sees significant conceptual problems in trying to reduce everything to bare bodily movements, perceptible surface irritations, and so on.

For one thing, that amounts to reforming language (as you yourself suggest when you talk of avoiding mixing psychological and physiological vocabularies). And Wittgenstein has no such wish; his aim is to get a clear view of language as it is used – and that certainly does not include deeming reports of mental events to be irrelevant. Such a claim suggests that it is ordinary language users who are confused when they say things like “the application came before her mind”. But the confusion lies with philosophers who fail to see the role of such statements and either (a) use them as the basis for quasi-Cartesian theories about mental realms, structures, etc, or (b) consider them a fiction and construct materialist theories about bare bodily movements, etc. For Wittgenstein, Behaviourism is the flip-side of dualism. Both are equally misguided.

For example, you say “A 'understood' your request as evidenced by her using the formula to provide one possible continuation of the provided fragment as you presumably intended”. What do you mean by “intended” here? Isn't this mixing psychological and physiological vocabularies? If not, then my “intention” must come down to behaviour. So what I intended is shown (to me and others) by what I did before and after my command. But if that's so then it's hard to say how I can know what I intended until I have observed my behaviour! So when I give a command I don't know what I intend by it until I've witnessed my behavioural response to A's attempt to follow the order. Except, of course, we now have a similar problem with “know”. For “knowing what I intended” is itself only to be cashed out in terms of behaviour. So I must observe my response to A's response to see what I intended and then observe my response to my response to make sure that I know what I intended. To put it mildly, that doesn't seem like a plausible account of what actually happens.

The root problem here is that Behaviourism claims everything is a matter of interpretation – in this case, the interpretation of behaviour. To say “A intended y” or “A understands y” is to have a theory about A inferred from observed behaviour. (The same ought to be true of “I understand y” but it's noteworthy that in practice the Behaviourist usually tacitly treats himself as a special case – see Daniel Dennett, for example.) But this is incoherent. There is such a thing as inferring someone's understanding based on an interpretation of their behaviour, but that stands in direct contrast to the huge number of cases where we don't do anything like that. To say that it's always like that is to misdescribe the concept of inferring (or “deriving”, “extrapolating” and so on). And to say it must be like that, even if we don't normally realise it, is to propose exactly the confused type of theory that Wittgenstein wants to warn us against.

Yet don't I propose circumstances as a key factor in justifying the statement “the application came before her mind”? I do. But isn't that (as you suggest) every bit as much an empirical claim as that understanding is caused by events in the brain? The answer to that turns on the fact that the word “justification” is used in a variety of different ways. It's not always a matter of inference. When I say that the circumstances help justify the claim I don't mean they provide a causal explanation of the behaviour. It's simply that in certain cases these circumstances licence us to say these things. The point is not a causal or theoretical one. It's a grammatical one.

To clarify, I don't subscribe to "Behaviorism" - or to any other "ism" because I typically don't know what characterizes one. When I look up an "ism" in SEP or IEP, I often find the large number of subcategories - and often sub-subcategories - more confusing than clarifying. In fact, according to the SEP entry, LW is arguably an "analytical/logical Behaviorist"! In any event, from the scenario in my last comment that begins with "Now suppose", it should be clear that I'm not taking a "strict Behaviorist" view since by hypothesis, a third party observer of your behavior would conclude that you didn't "understand" me whereas by my definition you did.

When I talk of "behavior", I'm using it descriptively - motor neurons fire and we twitch, ie, behave. I don't mean to "reduce everything" to observable behavior. Quite the contrary - as I've tried to make clear, I'm happy to "go inside". In fact, since dispositions aren't manifest until activated, it's actually necessary to do so, at least conceptually.

I don't get your point re "reforming" language. I think in terms of different vocabularies that are tailored to different purposes. As long as one sticks to the vocabulary appropriate to those narrow purposes, no problem. But I assume "ordinary language" is quotidian and includes words from so-called "folk psychology". IMO, such words should be used very carefully, if at all, once one transitions from the quotidian context to a more specialized one. In the former, "coming before the mind" can be like "a thought just popped into my mind" or "an old friend has been on my mind lately" in which "mind" is used in a way that everyone understands and accepts. But the discussion in PI §138-141 addresses the causal efficacy of specific images that "come before the mind". As far as I know, the causal efficacy of mental imagery is an open scientific question. Boundaries between areas of appropriate applicability of vocabularies are, of course, fuzzy and open to debate, but that use seems to me clearly a case of overstepping one.

You are correct that I mixed vocabularies, but for reasons of economy (a fancy way of saying I got lazy). To cash out "intent" in non-mentalese is a bit wordy, but here goes. You have had experiences that have resulted in dispositions to ask a certain question (or some member of a family of related questions) in certain contexts (in a very broad sense including externalities and internal bodily states) because doing so in the past has resulted in hearer responses that have been salutary for you. More generally, in your brain are associations between contexts, utterances, and hearer responses. So, saying that in a given context you act with "intent" to effect a result just means that you have a disposition to produce an utterance that is associated with that result.

Of course, all IMO. However, to short-circuit a standard criticism, I'll add that I don't mean to suggest that there is something akin to a table of such associations that rigidly specify a triad of context, utterance, and hearer response. In the candidate implementations of such dispositional structures of which I'm aware, there is "slop" in each member of that triad. Hence, the flexibility and adaptability that we clearly have.

This is a bit long, Charles, so I've had to divide it into two parts. Your comments are in italics.

In fact, according to the SEP entry, LW is arguably an "analytical/logical Behaviorist"!

Some have made that claim, but it's one I'd strongly reject. Wittgenstein stresses the importance of behaviour, but only as part of describing how we use words. He readily allows for sensations and all kinds of mental events and processes. What he objects to is philosophical theories that misunderstand the way such things are woven into lives via our language. But that's not to say that he has an alternative theory (eg, “logical behaviourism); he's simply pointing out that the way we use words like “meaning” and “understanding” doesn't square with the theories.

When I talk of "behavior", I'm using it descriptively - motor neurons fire and we twitch, ie, behave. I don't mean to "reduce everything" to observable behavior. Quite the contrary - as I've tried to make clear, I'm happy to "go inside". In fact, since dispositions aren't manifest until activated, it's actually necessary to do so, at least conceptually.

Whether or not it counts as behaviourism, my objection to this move is that it introduces a criterion of understanding (and meaning, intending and so on) which is quite patently not one we actually use. If the word “understanding” means a particular neural activity then we don't know whether someone understands unless we know that the neural activity has taken place. At best, therefore, we can only guess that someone understands – indeed, we can only guess that we understand. It would be possible for me to correctly follow a rule (so far as my actions go) throughout my adult life and yet still not actually understand it. Moreover, it would be possible for me to consistently follow the rule wrongly, yet understand it perfectly.

Here you might object that it can't be like that since it is the neuron-activity which causes the performance, so if the neuron state obtains then the correct result follows necessarily – but are you sure it's like that? It seems to me perfectly possible that different brains might achieve the same result via different neuron activity. Indeed, it seems possible that the same brain might achieve the same result via different neuron activity on different occasions. Are you sure that there is one thing that always happens in your brain every time you use the word “understand” correctly? And it's no help to say that we can infer which neuron states are the relevant ones by correlating them to correct behaviour, because it's supposed to be the neuron states which define correct behaviour, not the other way round!

In fact, that point remains even if it turns out there is one thing that always happens. We could only identify it by correlating it with what we already know to be correct usage. And if you do that then the neuron behaviour drops out as irrelevant.

I don't get your point re "reforming" language. I think in terms of different vocabularies that are tailored to different purposes. As long as one sticks to the vocabulary appropriate to those narrow purposes, no problem. But I assume "ordinary language" is quotidian and includes words from so-called "folk psychology". IMO, such words should be used very carefully, if at all, once one transitions from the quotidian context to a more specialized one.

My point here is that what you say amounts to reforming language! Behind it lurks the idea that what a word like “understanding” really means is something that – hopefully – science will one day reveal to us. So for now we soldier on with our “folk psychology” but in the future we might be able to use the word properly. And when we've reached that point we will indeed have reformed language.

This view, it seems to me, treats all words as “place holders”. So “understanding” means whatever science will one day explain to us in the same way that “dark matter” does (and “gene” used to). But the two cases are utterly different. “Dark matter” refers to a thing, but we don't yet know what that thing is (indeed, it may turn out to be a complete mistake, like the luminiferous aether). In that sense, the term is provisional. But there is nothing provisional about the way we use “understand”. We know what it is to correctly use the word; we know what it signifies. But it doesn't signify a thing – neither one we know about nor one we have yet to discover (let alone one we might discover doesn't exist). It is a word used according to certain criteria. And that's it.

Of course, it may one day happen that we do change the criteria for the word. And that change might be prompted by a neurological discovery. But the change of criteria would not itself be a discovery. We would simply be taking a decision to adopt a new terminology – presumably because it better suited our needs in some way. We wouldn't be discovering what the word “understand” really meant; we would be redefining it. In this respect, the whole materialist notion of “folk-psychology” is seriously misguided. “Love is blind” is a piece of folk-psychology; “I don't understand” is not.

Oops! THREE parts. Sorry for banging on at such length, but I felt you deserved a full reply to the good points you made.

But the discussion in PI §138-141 addresses the causal efficacy of specific images that "come before the mind". As far as I know, the causal efficacy of mental imagery is an open scientific question.

I hope what I've said above makes it clear that Wittgenstein is not dealing with causal efficacy here. As you say, that would be something for science to determine via experiment. He is making the logical point that pictures (or formulae, etc) are not intrinsically meaningful. Their meaning is something established via custom. We can establish that simply by reminding ourselves that the same picture can have different meanings in different situations (and that different pictures can have the same meaning). Therefore, “understanding” cannot amount to having a picture. Experiment is not needed.

You have had experiences that have resulted in dispositions to ask a certain question (or some member of a family of related questions) in certain contexts (in a very broad sense including externalities and internal bodily states) because doing so in the past has resulted in hearer responses that have been salutary for you. More generally, in your brain are associations between contexts, utterances, and hearer responses. So, saying that in a given context you act with "intent" to effect a result just means that you have a disposition to produce an utterance that is associated with that result.

Again, the problem here is that this either (a) introduces a criterion for “intend” which is currently beyond our reach, or (b) defines the relevant brain-state in terms of the outcome and is thus irrelevant from the point of view of correct usage. I suppose I could add (c) it is an unnecessarily theoretical way of saying that in certain circumstances I expect certain outcomes. Of course, no-one is disputing that.

[Introducing neural structures] introduces a criterion of understanding (and meaning, intending and so on) which is quite patently not one we actually use.

This and other responses suggest to me that I have not adequately explained the point of my alluding to different vocabularies, which in essence is to characterize who constitutes "we" (ie, the community in question) in such statements. So, think of a simple scenario in which there are three communities relevant to our exchange:

C1. Essentially all reasonably articulate speakers (of English) when engaged in every day discourse. The vocabulary of C1 (I call it "quotidian") includes words like "belief", "meaning", "mind", etc, the so-called "intentional idiom", "vocabulary of agency", or "mentalese", et al. (I prefer "mentalese" because it's short.) Among members of this community, mentalese is typically used without much thought. Responses to sentences like "what did you have in mind?" will be essentially reflexive with little or no consideration of what "have in mind" might mean in terms of pictures, behavior, neurology, etc.

C2. The subset of C1 that tries to think deeply about how language works, eg, ala PI. The vocabulary of C2 will be the quotidian vocabulary augmented by some phil-of-mind-specific jargon. Behavior, especially the use of words in general and mentalese in particular, will be given a lot of attention.

C3. The subset of C2 that tries to think about what physiological processes might produce behavior. The vocabulary of C3 includes additional specialized vocabularies such as that of neurology, but excludes mentalese to the maximum extent possible because from a physiological perspective many words of mentalese arguably don't refer (eg, "mind"). However, in order to facilitate interchange between members of C2 who aren't members of C3 and members of C2 who are, a member of C3 may occasionally attempt to cash out in some specialized vocabulary the general concept behind a mentalese word.

This is pretty much the scenario I assume when thinking about these issues. I hope it makes clear that I am not:

- suggesting "reforming" the quotidian vocabulary of C1 in which it works just fine. Nor am I suggesting reforming the expanded vocabulary of C2 which works just fine in that community. However, I am suggesting that care should be taken that discourse in the vocabulary of C2 not be slipped into discourse for which the vocabulary of C3 is more appropriate.

- proposing hypothetical criteria defined in the vocabulary of C3 for the appropriate use of mentalese in C2

- suggesting that what a mentalese word "really means" may some day be expressed in the vocabulary of C3, since IMO "meaning" is not an appropriate word for that vocabulary.

Having now reread PI §138-141 numerous times and 20+ subsequent sections, I realize that I don't always follow the transitions between author and interlocutor, a problem exacerbated by your explanation that the interlocutor in §138-141 is "early-W". Thus, I may well be attributing to PI author "later-W" statements properly attributed to "early-W", ie, just piling on after the play is over. So, I'm withdrawing my complaint about those sections.

You're right, of course, that specialist groups tend to develop specialised vocabularies. That's true of neuroscientists, bird-watchers and chess-players. There's nothing wrong with this in itself, so long as we're clear about the relationship between the specialised vocabulary and our normal forms of expression. Philosophical problems can arise when we conflate the two without realising it (and that's especially true regarding scientific vocabularies).

However, there's another source of philosophical puzzlement: failure to see clearly how our normal forms of expression are used. So, for example, if you assume that the word “understanding” functions as a name then you will be led to search for the thing that it names. Is it a mental picture? A thought? Or a mental disposition or structure? Or is it a physical disposition or structure – in the brain, perhaps? You will start to produce all kinds of theories (probably couched in technical jargon) and may well look to science for assistance.

At this point, you will have joined the second community on your list: the people who “think deeply about how language works”. But, of course, if the word “understanding” isn't actually used as a name then the whole investigation is a wild goose-chase. All the ingenious theories, with their technical terms and appeals to scientific discoveries, will be in vain. You are chasing shadows.

And this, from a Wittgensteinian perspective, is precisely the position of philosophy of language and consciousness studies today. They are elaborate houses of cards based on fundamental misunderstandings about a whole range of interrelated concepts such as “mind”, “thought”, “meaning”, “understanding”, “intention”, “will”, and so on. It is not that they have a richer understanding than ordinary people (with a specialist vocabulary to match it). Rather, they have a set of confusions upon which they have erected a formidable-looking edifice of theoretical doctrine.

Far from accepting this edifice as a deeper approach, the whole Wittgensteinian task is to expose its emptiness and bring it back to its “quotidian” roots. And this isn't done by proposing new theories or unearthing new facts. It's done by reminding us of what we, as competent language-users, already know: how words are used in everyday life.

A couple of further points. First, I'd be careful of using “mentalese” to mean talk of mental phenomena. It's more commonly used to denote the “pre-verbal” language (or “language of thought”) which some theories claim must be a precondition of verbalisation (Chomsky and Pinker both subscribe to variations on this idea). “I've something on my mind” is not an example of mentalese.

Finally, I can sympathise with your difficulty over identifying Wittgenstein's interlocutor. There are some passages where it's very hard indeed to distinguish between the two.

Well, Philip, this may be the end of our exchange since I pretty much agree with your last comment! Just a couple of clarifications:

if you assume that the word “understanding” functions as a name ...

That one shouldn't assume this is the idea I meant to convey by writing "from a physiological perspective many words of [the intentional idiom] arguably don't refer". Better to avoid such terms if possible in C3 discussions. (Thanks for the suggestion re "mentalese".)

At this point, you will have joined the second community on your list: the people who “think deeply about how language works”.

I actually meant C2 to be you Wittgensteinians who think deeply in the "right" way. I should have added an explicit community the members of which have one foot in each of C2 and C3 in that they use the intentional idiom while occasionally straying into areas arguably better addressed in the vocabulary of C3.

Thanks Charles. I do appreciate you taking the time to comment on this stuff. What we've been discussing anticipates some of the upcoming points about understanding (in fact, it's helped me clarify my thoughts) so you might find it strangely familiar!